03177nam 2200529 450 991081898270332120170918220518.00-8218-9994-5(CKB)3360000000463968(EBL)3113715(SSID)ssj0000976585(PQKBManifestationID)11569855(PQKBTitleCode)TC0000976585(PQKBWorkID)11019844(PQKB)11202271(MiAaPQ)EBC3113715(RPAM)0000000637(PPN)195408888(EXLCZ)99336000000046396820750404h19511951 uy| 0engur|n|---|||||txtccrTheory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields /Oscar ZariskiProvidence, Rhode Island :American Mathematical Society,[1951]©19511 online resource (99 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 5 (1951)Cover title.0-8218-1205-X Includes bibliographical references.""Contents""; ""Introduction""; ""Part I: General Theory of Holomorphic Functions""; ""1. Strongly holomorphic functions""; ""2. Strongly holomorphic functions on afflne models""; ""3. The general concept of a holomorphic function""; ""4. Rational holomorphic functions. Some unsolved problems""; ""5. Digression on algebraic points""; ""6. Holomorphic functions, analytical irreducibility and a connectedness criterion""; ""7. Analytical Irreducibility and normalization""; ""8. Some lemmas on m-adic rings""; ""9. Holomorphic functions on afflne models""""Part II: Invariance of Rings of Holomorphic Functions under Rational Transformations""""10. Holomorphic functions and semi-regular birational transformations""; ""11. Absolute birational Invariance of rings of holomorphic functions""; ""12. Reduction of the proof of the fundamental theorem to a special case""; ""13. The birational transformation V --> Vot""; ""14. Proof of the fundamental theorem in the case of the transformation V --> Vot""; ""15. Last step of the proof of the fundamental theorem: transition to the derived normal model Vot""""16. Extension of the fundamental theorem to rational transformations""""17. Reduction of the proof to a special case""; ""18. The rational transformation V --> Vot""; ""19. The transformation Vot --> Vot""; ""Part III: The Principle of Degeneration""; ""20. A connectedness theorem for algebraic correspondences""; ""21. Algebraic systems of r-cycles""; ""22. Proof of the principle of degeneration""Memoirs of the American Mathematical Society ;number 5.Algebraic functionsAlgebraic functions.Zariski Oscar42025MiAaPQMiAaPQMiAaPQBOOK9910818982703321Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields335962UNINA